Null warped AdS in higher spin gravity

TL;DR

This paper introduces new boundary conditions for three-dimensional higher spin gravity, revealing a chiral symmetry algebra and analyzing thermodynamic properties, thus advancing the understanding of null warped AdS geometries.

Contribution

It establishes asymptotically null warped AdS boundary conditions in higher spin gravity and uncovers the associated chiral Polyakov-Bershadsky algebra as the asymptotic symmetry.

Findings

Identified a chiral Polyakov-Bershadsky algebra as the asymptotic symmetry.

Constructed a global gauge transformation linking to AdS spin-3 gravity.

Derived thermodynamic quantities like entropy and free energy.

Abstract

We equip three-dimensional spin-3 gravity in the principal embedding with a new set of boundary conditions that we call "asymptotically null warped AdS". We find a chiral copy of the Polyakov-Bershadsky algebra as asymptotic symmetry algebra, reminiscent of the situation in topologically massive gravity with strict null warped AdS boundary conditions. We prove the invertibility of the map between zuvielbein and metric variables and construct a global gauge transformation to half of AdS spin-3 gravity in the diagonal embedding. This explains why the theory is chiral and why the Polyakov-Bershadsky algebra arises. We then introduce chemical potentials, derive the entropy, free energy, and the holographic response functions, and conclude with a discussion.